Enzymes are amphoteric molecules containing a large number of acid and basic
groups, mainly situated on their surface. The charges on these groups will vary,
according to their acid dissociation constants, with the pH of their environment
(Table 1.1).
This will effect the total net charge of the enzymes and the distribution of
charge on their exterior surfaces, in addition to the reactivity of the
catalytically active groups. These effects are especially important in the
neighbourhood of the active sites. Taken together, the changes in charges with
pH affect the activity, structural stability and solubility of the enzyme.

Table 1.1. pKasa
and heats of ionisationb
of the ionising groups commonly found in enzymes.

Group

Usual pKa
range

Approximate charge at
pH 7

Heats of ionisation
(kJ mole-1)

Carboxyl (C-terminal, glutamic acid,
aspartic acid)

3 - 6

-1.0

±
5

Ammonio (N-terminal) (lysine)

7 - 9

+1.0

+45

9 - 11

+1.0

+45

Imidazolyl (histidine)

5 - 8

+0.5

+30

Guanidyl (arginine)

11 - 13

+1.0

+50

Phenolic (tyrosine)

9 - 12

0.0

+25

Thiol (cysteine)

8 - 11

0.0

+25

aThe pKa (defined
as -Log10(Ka)) is the pH at which half the groups are
ionised. Note the similarity between the Ka of an acid and the Km
of an enzyme, which is the substrate concentration at which half the enzyme
molecules have bound substrate.

b By convention, the heat (enthalpy)
of ionisation is positive when heat is withdrawn from the surrounding solution
(i.e. the reaction is endothermic) by the dissociation of the hydrogen ions.

There will be a pH, characteristic of each
enzyme, at which the net charge on the molecule is zero. This is called the
isoelectric point (pI), at which the enzyme generally has minimum solubility in
aqueous solutions. In a similar manner to the effect on enzymes, the charge and
charge distribution on the substrate(s), product(s) and coenzymes (where
applicable) will also be affected by pH changes. Increasing hydrogen ion
concentration will, additionally, increase the successful competition of
hydrogen ions for any metal cationic binding sites on the enzyme, reducing the
bound metal cation concentration. Decreasing hydrogen ion concentration, on the
other hand, leads to increasing hydroxyl ion concentration which compete against
the enzymes' ligands for divalent and trivalent cations causing their conversion
to hydroxides and, at high hydroxyl concentrations, their complete removal from
the enzyme. The temperature also has a marked effect on ionisations, the extent
of which depends on the heats of ionisation of the particular groups concerned (Table
1.1). The relationship between the change in the pKa and the
change in temperature is given by a derivative of the Gibbs-Helmholtz equation:

(1.12)

where T is the absolute temperature (K), R is
the gas law constant (8.314 J M-1 K-1), DH is the heat of ionisation and
the numeric constant (2.303) is the natural logarithm of 10, as pKa's
are based on logarithms with base 10. This variation is sufficient to shift the
pI of enzymes by up to one unit towards lower pH on increasing the temperature
by 50°C.

These charge variations, plus any consequent
structural alterations, may be reflected in changes in the binding of the
substrate, the catalytic efficiency and the amount of active enzyme. Both Vmax
and Km will be affected due to the resultant modifications to the
kinetic rate constants k+1, k-1 and kcat (k+2
in the Michaelis-Menten mechanism), and the variation in the concentration of
active enzyme. The effect of pH on the Vmax of an enzyme catalysed
reaction may be explained using the, generally true, assumption that only one
charged form of the enzyme is optimally catalytic and therefore the maximum
concentration of the enzyme-substrate intermediate cannot be greater than the
concentration of this species. In simple terms, assume EH- is the
only active form of the enzyme,

[1.8]

The concentration of EH- is
determined by the two dissociations

[1.9]

[1.10]

with

(1.13)

and

(1.14)

However,

(1.15)

therefore:

(1.16)

As the rate of reaction is given by k+2[EH-S]
and this is maximal when [EH-S] is maximal (i.e.. when [EH-S]
= [EH-]0):

(1.17)

The Vmax will be greatest when

(1.18)

therefore:

(1.19)

This derivation has involved a number of
simplifications on the real situation; it ignores the effect of the ionisation
of substrates, products and enzyme-substrate complexes and it assumes EH-
is a single ionised species when it may contain a mixture of differently ionised
groups but with identical overall charge, although the process of binding
substrate will tend to fix the required ionic species. It does, however, produce
a variation of maximum rate with pH which gives the commonly encountered 'bell-shaped'
curve (Figure
1.4). Where the actual reaction scheme is more complex, there may be a more
complex relationship between Vmax and pH. In particular, there may be
a change in the rate determining step with pH. It should be recognised that Km
may change with pH in an independent manner to the Vmax as it usually
involves other, or additional, ionisable groups. It is clear that at lower non-saturating
substrate concentrations the activity changes with pH may or may not reflect the
changes in Vmax. It should also be noted from the foregoing
discussion that the variation of activity with pH depends on the reaction
direction under consideration. The pHoptimum may well be different in
the forward direction from that shown by the reverse reaction. This is
particularly noticeable when reactions which liberate or utilise protons are
considered (e.g. dehydrogenases) where there may well be greater than 2 pH units
difference between the pHoptimum shown by the rates of forward and
reverse reactions.

Figure 1.4. A generally applicable schematic diagram of
the variation in the rate of an enzyme catalysed reaction (Vmax) with
the pH of the solution. The centre (optimum pH) and breadth of this 'bell-shaped'
curve depend upon the acid dissociation constants of the relevant groups in the
enzyme. It should be noted that some enzymes have pH-activity profiles that show
little similarity to this diagram.

The variation of activity with pH, within a
range of 2-3 units each side of the pI, is normally a reversible process.
Extremes of pH will, however, cause a time- and temperature-dependent,
essentially irreversible, denaturation. In alkaline solution (pH > 8), there may
be partial destruction of cystine residues due to base catalysed b-elimination reactions whereas,
in acid solutions (pH < 4), hydrolysis of the labile peptide bonds, sometimes
found next to aspartic acid residues, may occur. The importance of the knowledge
concerning the variation of activity with pH cannot be over-emphasised. However,
a number of other factors may mean that the optimum pH in the Vmax-pH
diagram may not be the pH of choice in a technological process involving enzymes.
These include the variation of solubility of substrate(s) and product(s),
changes in the position of equilibrium for a reaction, suppression of the
ionisation of a product to facilitate its partition and recovery into an organic
solvent, and the reduction in susceptibility to oxidation or microbial
contamination. The major such factor is the effect of pH on enzyme stability.
This relationship is further complicated by the variation in the effect of the
pH with both the duration of the process and the temperature or temperature-time
profile. The important parameter derived from these influences is the
productivity of the enzyme (i.e. how much substrate it is capable of converting
to product). The variation of productivity with pH may be similar to that of the
Vmax-pH relationship but changes in the substrate stream composition
and contact time may also make some contribution. Generally, the variation must
be determined under the industrial process conditions. It is possible to alter
the pH-activity profiles of enzymes. The ionisation of the carboxylic acids
involves the separation of the released groups of opposite charge. This process
is encouraged within solutions of higher polarity and reduced by less polar
solutions. Thus, reducing the dielectric constant of an aqueous solution by the
addition of a co-solvent of low polarity (e.g. dioxan, ethanol), or by
immobilisation , increases the pKa of carboxylic acid groups. This
method is sometimes useful but not generally applicable to enzyme catalysed
reactions as it may cause a drastic change on an enzyme's productivity due to
denaturation . The pKa of basic groups are not similarly affected as
there is no separation of charges when basic groups ionise. However, protonated
basic groups which are stabilised by neighbouring negatively charged groups will
be stabilised (i.e. have lowered pKa) by solutions of lower polarity.
Changes in the ionic strength (I)
of the solution may also have some effect. The ionic strength is defined as half
of the total sum of the concentration (ci) of every ionic species (i)
in the solution times the square of its charge (zi); i.e.
. I = 0.5S(cizi2).
For example, the ionic strength of a 0.1 M solution of CaCl2 is 0.5 x
(0.1 x 22 + 0.2 x 12) = 0.3 M.
At higher solution ionic strength, charge separation is encouraged with a
concomitant lowering of the carboxylic acid pKas. These changes,
extensive as they may be, have little effect on the overall charge on the enzyme
molecule at neutral pH and are, therefore, only likely to exert a small
influence on the enzyme's isoelectric point. Chemical derivatisation methods are
available for converting surface charges from positive to negative and vice-versa.
It is found that a single change in charge has little effect on the pH-activity
profile, unless it is at the active site. However if all lysines are converted
to carboxylates (e.g. by reaction with succinic anhydride) or if all the
carboxylates are converted to amines (e.g. by coupling to ethylene diamine by
means of a carbodiimide, ) the profile can be shifted about a pH unit towards
higher or lower pH, respectively. The cause of these shifts is primarily the
stabilisation or destabilisation of the charges at the active site during the
reaction, and the effects are most noticeable at low ionic strength. Some, more
powerful, methods for shifting the pH-activity profile are specific to
immobilised enzymes and described .

The ionic strength of the solution is an
important parameter affecting enzyme activity. This is especially noticeable
where catalysis depends on the movement of charged molecules relative to each
other. Thus both the binding of charged substrates to enzymes and the movement
of charged groups within the catalytic 'active' site will be influenced by the
ionic composition of the medium. If the rate of the reaction depends upon the
approach of charged moieties the following approximate relationship may hold,

(1.20)

where k is the actual rate constant, k0
is the rate constant at zero ionic strength, zA and zB are
the electrostatic charges on the reacting species, and v is the ionic strength
of the solution. If the charges are opposite then there is a decrease in the
reaction rate with increasing ionic strength whereas if the charges are
identical, an increase in the reaction rate will occur (e.g. the rate
controlling step in the catalytic mechanism of chymotrypsin involves the
approach of two positively charged groups, 57histidine+
and 145arginine+ causing a significant increase in kcat
on increasing the ionic strength of the solution). Even if a more complex
relationship between the rate constants and the ionic strength holds, it is
clearly important to control the ionic strength of solutions in parallel with
the control of pH.